1. Field of the Invention
The present invention relates generally to ionospheric modeling, and in particular, to a method, apparatus, and article of manufacture for analyzing ionospheric slant total electron content (TEC) using global positioning system (GPS) based estimation.
2. Description of the Related Art
(Note: This application may reference a number of different publications as indicated throughout the specification. A list of these different publications as well as references that may be relevant to the present invention can be found below in the section entitled “References.” Each of these publications is incorporated by reference herein.)
For single-frequency users of global navigation satellite systems (GNSS), ionospheric delay continues to be the largest source of positioning error. In this regard, free electrons along the raypath impede the passage of a GNSS signal through the ionosphere. The total delay is proportional to the slant total electron content (STEC) along the raypath. The issue arises regarding how to analyze and visualize ionospheric STEC using measurements of GNSS. To understand such issues better, a description of prior art position estimating systems may be useful.
To guarantee the safety of airline navigation based upon GNSS signals, satellite-based augmentation systems (SBAS) have been developed to ensure the accuracy, integrity, availability, and continuity of user position estimates derived from GNSS measurements. In the United States, the Wide Area Augmentation System (WAAS) is an augmentation of the Global Positioning System (GPS) that measures the ionospheric slant delay of signals propagating from GPS satellites to multiple, dual frequency receivers distributed across North America in a network of thirty-eight reference stations (see FIG. 1).
To allow the user to correct for the error due to ionospheric delay, WAAS derives from these measurements a vertical delay estimate at each ionospheric grid point (IGP) in a mask specified by the WAAS Minimum Operational Performance Standards [MOPS, 2001] (see FIG. 2). The vertical delay at an IGP is designated the Ionospheric Grid Delay (IGD) at that IGP. In addition, WAAS computes, at each IGP, a safety-critical integrity bound called the Grid Ionospheric Vertical Error (GIVE). Integrity refers to the reliability and trustworthiness of the information provided by the navigation system and to the system's ability to deliver timely warnings to users when the system should not be used for navigation because of signal corruption or some other error or failure in the system. GIVEs are derived from inflated and augmented values of the formal estimation error. They protect the user from the effects of delay estimation error due to ionospheric irregularity, both sampled and undersampled.
From the Initial Operating Capability of WAAS in July of 2003 through Release 8/9 of the initial system to newer systems, the vertical delay estimate and its integrity bound at each IGP have been calculated from a planar fit of slant delay measurements projected to vertical. The slant-to-vertical conversion is achieved by modeling the ionosphere as an infinitesimally thin shell at a representative ionospheric altitude (see FIG. 3). In a later version of WAAS, estimation of vertical delays is performed by a geo-statistical technique known as kriging [Cressie, 1993; Webster, 2001; Blanch, 2002; Wackernagel, 2003], a type of minimum mean square estimator, adapted to spatial data, that originated in the mining industry in the 1950's. Kriging provides a smoothed depiction of a spatially distributed variable that has been sampled by irregularly spaced measurements. Compared to the planar fit model, the kriging model generally achieves a better match to the observed random structure of the vertical delays (or it can be tuned to match these data better).
To calculate the IGDs and GIVEs, WAAS (as well as the European Geostationary Navigation Overlay Service [EGNOS]) models the ionosphere as an infinitesimally thin shell at a representative ionospheric altitude (referred to as the thin shell model). The thin shell model is a crude model where the electron density is assumed to be non-negligible only in an infinitesimally thin layer located at a shell height representative of the altitude where the electron density attains its peak value. Such a crude approximation necessarily introduces error into delay estimation.
The thin shell model serves two purposes: (1) to define the ionospheric pierce point (IPP) of each measurement; and (2) to convert the slant delay measurement to a vertical delay estimate at the IPP. An IPP is the location where a satellite-to-station raypath or a satellite-to-user-receiver raypath penetrates the thin shell. At regularly spaced intervals in time, WAAS performs delay estimation, converting slant delay measurements in a given epoch to vertical delay estimates and transforms these vertical delay estimates, distributed unevenly in space over the thin shell, into a set of vertical delay estimates distributed at regular spatial intervals on the WAAS ionospheric grid. To infer the ionospheric slant delay (and its integrity bound) associated with a GPS signal detected by the user's receiver, the user must first determine the IPP associated with the signal and then approximate the vertical delay at this IPP using bilinear interpolation of the IGDs (and their integrity bounds) at the nearest IGPs surrounding the IPP. The interpolated vertical delay estimate is then converted, again using the thin shell model, to an estimate of the slant delay from the satellite to the user.
With a slant delay estimate and integrity bound for each GPS signal detected by a user's receiver, the user can determine a correction to his or her position estimate and an integrity bound on that estimate. This integrity bound is used, in turn, to specify the user's Horizontal Protection Level (HPL) and Vertical Protection Level (VPL). The HPL and VPL are the receiver-computed integrity bounds defined by the MOPS [2001] as, respectively, the radius of a circle in the horizontal plane and the half-length of a segment on the vertical axis perpendicular to this plane, each describing a region whose center coincides with the user's true position and whose breadth is sufficient to provide assurance that the region contains the estimated position. The HPL and VPL define the regions in which the respective time-to-alert requirements can be met. A Horizontal Alert Limit (HAL) and, where applicable, a Vertical Alert Limit (VAL) are associated with each navigation mode (e.g., precision approach, non-precision approach, en route, etc.) supported by WAAS. The MOPS [2001] defines the HAL and VAL as, respectively, a radius and segment half-length, analogous to the HPL and VPL, each describing regions also centered on the user's position but of such breadth as to meet the requirement to contain the true position within the probability required for a particular navigation mode. When the HPL exceeds the HAL or the VPL exceeds the VAL for a given level of aviation service, that level of service is not available to the user. When the true error in a user's position exceeds the VAL (for equipment aware of the navigation mode) or the computed VPL (for equipment not aware) and WAAS fails to provide notification of the error within the time-to-alert of the applicable phase of flight, WAAS is considered to be broadcasting hazardously misleading information (HMI). For example, the most restrictive integrity requirement on WAAS is that the upper bound on the probability of broadcasting hazardously misleading information be no more than one occurrence in every 10,000,000 runway approaches (resulting in either landings or missed approaches) that use precision approach with vertical guidance, i.e., a probability of broadcasting hazardously misleading information of 10−7.
By this means, WAAS provides vertical guidance down to a minimum height above the runway as determined by the level of the aviation service. The decision height in a precision approach is the height at which a missed approach must be initiated if the required visual reference to continue the approach has not been established. Each level of aviation service specifies a distinct decision height and VAL. For Localizes Performance with Vertical guidance (LPV) service, the decision height is 250 feet and the VAL is 50 meters; for LPV200 service, the decision height is 200 feet, and the VAL is 35 meters.
As described above, in its initial operational capability, WAAS performed vertical delay estimation by incorporating the thin shell model into a planar fit algorithm. A later version of WAAS replaced the planar fit algorithm with an algorithm based upon a geo-statistical technique known as kriging. The success of kriging is partly due to its ability to mitigate the error due to the thin shell approximation. Other alternative methods of delay estimation eliminate the need for adopting the thin shell approximation altogether.
However, even though WAAS and other systems are capable of performing delay estimation, such prior methods fail to provide a delay estimation method that is efficient and sufficiently removes one or more sources of error. Regardless of the method utilized to mitigate error, it is useful to have a system that allows the user to analyze and visualize the ionospheric STEC using GNSS. In other words, it is useful to have a system that measures/evaluates the accuracy of the method utilized and determine STEC.